Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions

In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisps motion as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.Comment: 30 pages, 12 figure

Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited

Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1.Comment: 14 pages, 9 figures, accepted for publication (MNRAS

Relativistic Jets and Long-Duration Gamma-ray Bursts from the Birth of Magnetars

We present time-dependent axisymmetric magnetohydrodynamic simulations of the interaction of a relativistic magnetized wind produced by a proto-magnetar with a surrounding stellar envelope, in the first $\sim 10$ seconds after core collapse. We inject a super-magnetosonic wind with $\dot E = 10^{51}$ ergs s$^{-1}$ into a cavity created by an outgoing supernova shock. A strong toroidal magnetic field builds up in the bubble of plasma and magnetic field that is at first inertially confined by the progenitor star. This drives a jet out along the polar axis of the star, even though the star and the magnetar wind are each spherically symmetric. The jet has the properties needed to produce a long-duration gamma-ray burst (GRB). At $\sim 5$ s after core bounce, the jet has escaped the host star and the Lorentz factor of the material in the jet at large radii $\sim 10^{11}$ cm is similar to that in the magnetar wind near the source. Most of the spindown power of the central magnetar escapes via the relativistic jet. There are fluctuations in the Lorentz factor and energy flux in the jet on $\sim 0.01-0.1$ second timescale. These may contribute to variability in GRB emission (e.g., via internal shocks).Comment: 5 pages, 3 figures, accepted in MNRAS letter, presented at the conference "Astrophysics of Compact Objects", 1-7 July, Huangshan, Chin

Relativistic MHD modeling of magnetized neutron stars, pulsar winds, and their nebulae

Neutron stars are among the most fascinating astrophysical sources, being characterized by strong gravity, densities about the nuclear one or even above, and huge magnetic fields. Their observational signatures can be extremely diverse across the electromagnetic spectrum, ranging from the periodic and low-frequency signals of radio pulsars, up to the abrupt high-energy gamma-ray flares of magnetars, where energies of ~10^46 erg are released in a few seconds. Fast-rotating and highly magnetized neutron stars are expected to launch powerful relativistic winds, whose interaction with the supernova remnants gives rise to the non-thermal emission of pulsar wind nebulae, which are known cosmic accelerators of electrons and positrons up to PeV energies. In the extreme cases of proto-magnetars (magnetic fields of ~10^15 G and millisecond periods), a similar mechanism is likely to provide a viable engine for the still mysterious gamma-ray bursts. The key ingredient in all these spectacular manifestations of neutron stars is the presence of strong magnetic fields in their constituent plasma. Here we will present recent updates of a couple of state-of-the-art numerical investigations by the high-energy astrophysics group in Arcetri: a comprehensive modeling of the steady-state axisymmetric structure of rotating magnetized neutron stars in general relativity, and dynamical 3-D MHD simulations of relativistic pulsar winds and their associated nebulae.Comment: EPS 44th Conference on Plasma Physics (June 2017, Belfast), paper accepted for publication on Plasma Physics and Controlled Fusio

MHD Interaction of Pulsar Wind Nebulae with SNRs and the ISM

In the late 1960s the discovery of the Crab pulsar in its associated supernova remnant, launched a new field in supernova remnant research: the study of pulsar-driven or plerionic supernova remnants. In these type of remnants, the relativistic wind emitted by the pulsar, blows a pulsar wind nebula into the interior of its supernova remnant. Now, more then forty years after the discovery of the Crab pulsar, there are more then fifty plerionic supernova remnants known, due to the ever-increasing capacity of observational facilities. I will review our current understanding of the different evolutionary stages of a pulsar wind nebula as it is interacting with its associated supernova remnant.Therefore I will discuss both analytical and more recent numerical (M)HD models.The four main stages of a pulsar wind nebula are: the supersonic expansion stage, the reverse shock interaction stage, the subsonic expansion stage and ultimatelythe stage when the head of the bubble is bounded by a bow shock, due to the supersonic motion of the pulsar. Ultimately this pulsar wind nebula bow shock will break through its associated remnant, after which the pulsar-powered bow shock will interact directly with the interstellar medium. I will discuss recent numerical models from these type of pulsar wind nebulae and their morphology.Comment: 11 pages, 3 figures, Advances in Space Research, in pres

Polarization in the inner region of Pulsar Wind Nebulae

We present here the first effort to compute synthetic synchrotron polarization maps of Pulsar Wind Nebulae (PWNe). Our goal is to highlight how polarization can be used as an additional diagnostic tool for the flow structure in the inner regions of these nebulae. Recent numerical simulations suggest the presence of flow velocities ~0.5 c in the surroundings of the termination shock, where most of the high energy emission comes from. We construct polarization maps taking into account relativistic effects like Doppler boosting and position angle swing. The effect of different bulk velocities is clarified with the help of a toy-model consisting of a uniformly emitting torus. We also present a map based on recent numerical simulations of the entire nebula and compare it with presently available data. The comparison with upcoming high resolution observations could provide new insight into the inner structure of the nebula and put constraints on the geometrical properties of the magnetic field.Comment: Accepted for publication on A&A, 6 pages, 2 figure

Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid

We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector \beta, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the \beta frame and Landau frame and present an instance where they differ.Comment: 22 pages, 3 figures. To appear in Eur. Phys. J.

Simulated synchrotron emission from Pulsar Wind Nebulae

A complete set of diagnostic tools aimed at producing synthetic synchrotron emissivity, polarization, and spectral index maps from relativistic MHD simulations is presented. As a first application we consider here the case of the emission from Pulsar Wind Nebulae (PWNe). The proposed method is based on the addition, on top of the basic set of MHD equations, of an extra equation describing the evolution of the maximum energy of the emitting particles. This equation takes into account adiabatic and synchrotron losses along streamlines for the distribution of emitting particles and its formulation is such that it is easily implemented in any numerical scheme for relativistic MHD. Application to the axisymmetric simulations of PWNe, analogous to those described by Del Zanna et al. (2004, A&A, 421, 1063), allows direct comparison between the numerical results and observations of the inner structure of the Crab Nebula, and similar objects, in the optical and X-ray bands. We are able to match most of the observed features typical of PWNe, like the equatorial torus and the polar jets, with velocities in the correct range, as well as finer emission details, like arcs, rings and the bright knot, that turn out to arise mainly from Doppler boosting effects. Spectral properties appear to be well reproduced too: detailed spectral index maps are produced for the first time and show softening towards the PWN outer borders, whereas spectral breaks appear in integrated spectra. The emission details are found to strongly depend on both the average wind magnetization (here approximately 2%), and on the magnetic field shape.Comment: 14 pages, submitted to A&

Contribution to Galactic cosmic rays from young stellar clusters

The origin of Galactic cosmic rays (CR) is still a matter of debate. Diffusive shock acceleration (DSA) applied to supernova remnant (SNR) shocks provides the most reliable explanation. However, within the current understanding of DSA several issues remain unsolved, like the CR maximum energy, the chemical composition and the transition region between Galactic and extra-Galactic CRs. These issues motivate the search for other possible Galactic sources. Recently, several young stellar clusters (YSC) have been detected in gamma rays, suggesting that such objects could be powerful sources of Galactic CRs. The energy input could come from winds of massive stars hosted in the clusters which is a function of the cluster total mass and initial mass function of stars. In this work we evaluate the total CR flux produced by a synthetic population of YSCs assuming that the CR acceleration occurs at the termination shock of the collective wind resulting from the sum of cluster's stellar winds. We show that the spectrum produced by YSC can significantly contribute to energies $\gtrsim 100$ TeV if the diffusion inside the wind-blown bubble is Bohm-like and the spectral slope is harder than the one produced by SNRs.Comment: Proceeding to the International Cosmic Ray Conference, ICRC 2023, Nagoya, Japa